Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ? 1 -regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ? 1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai–Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ? 1 minimization method in both spatial aggregation and location accuracy.

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X‐ray luminescence computed tomography (XLCT) uses external X‐rays for luminescence excitation, which is becoming a promising molecular imaging technique with superb penetration depth and spatial resolution. To achieve the tomographic mapping of luminescence distribution, accurate optical propagation model and suitable reconstruction method are two keys for XLCT, but not satisfied. To overcome the limitation of the single proton propagation model (e.g., DE, SP3), we adopted a hybrid diffusion equation with third order simplified spherical harmonics (DE‐SP3) model for XLCT. To enable fast iteration and accurate sparse reconstruction, we also integrated in the inversion optimization, with a novel Least Square QR‐factorization based on the Lasso (Lasso‐LSQR) algorithm. We first simulated the light propagation in various kinds of organs under DE model and SP3 model, respectively. By comparison with the Monte Carlo, these tissues can be categorized into two types, namely DE‐fitted tissues that include muscle and lung, and SP3‐fitted tissues including heart, kidney, liver, and stomach. According to the above classification results, we built a hybrid DE‐SP3 model to more accurately describing light transport. Numerical simulations and in vivo experiments illustrated that hybrid DE‐SP3 model achieves superior reconstruction performance in terms of location accuracy, and spatial resolution than DE, and less computational cost than SP3. The hybrid DE‐SP3 model materializes a balance between accuracy and efficiency for XLCT.

Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L1-L2 norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L1-L2 norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L1-L2 norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

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